Marcu 24, 1923] 
NATURE 
397 

the lowest and highest tension. In a good section of 
the cochlea set ka ligament will be seen to exhibit 
a progressive differentiation in bulk and closeness of 
texture not inconsistent with such extremes of tension. 
Further, the upper and lower limit of tension can be 
roughly calculated, and the resulting values are 
possible ones. The highest is only about a quarter 
of the breaking strain of tendinous structures of the 
same fineness. 
Helmholtz recognised quite clearly the bearing of 
the “ load ”’ on the basilar fibres in rendering possible 
the small scale of the cochlea, though he failed to 
realise the progressive differentiation of the fibres for 
mass thereby effected. He says, ‘‘ That such short 
strings should be capable of corresponding with such 
deep tones must be explained by their being loaded 
in the basilar membrane with all kind of solid forma- 
tions ; the fluid of both galleries in the cochlea must 
also be considered as weighting the membrane, because 
it cannot move without a kind of wave motion in that 
fluid” (second English edition translated by A. J. 
Ellis, p. 146). F 
-No doubt if Helmholtz had known the anatomical 
structure of the spiral ligament, which was described 
_ by Albert Gray in 1900, the whole mechanism of the 
cochlea would have been clear to him. 
GEORGE WILKINSON. 
387 Glossop Road, Sheffield. 

Stirling’s Theorem. 
In starting from dn=1 and then making dn infini- 
tesimal, Dr. Satterly’s demonstration in NatTuRE of 
February 17, p. 220, is scarcely convincing, and the 
error introduced by this step is represented in his 
answer by the absence of the factor 1/./n or the term 
} log , neither of which is entirely negligible when 
is large. I suggest the following adaptation of his 
proof, which avoids, I think, the inconsistency referred 
to above. 
Log |n +1 —log|n=log (n +1). 
.. by Taylor’s theorem 
(D+D*/|2+.. 
all terms on the right being negligible after the first 
when » is large. 
- )log|n=logn+1/n+... 
-. log n= log 
z 
D+D*/\2+.. 
=p (1 -D/2 +kD* +) logn 
= flogndn-}flogn+kin+... 
=nlogn-n-tlogn +C. 
The constant can readily be evaluated by the use 
of Wallis’s expression for 7. 
JAMES STRACHAN, 
. 20 Woodside Terrace, Darlington, 
February 23. 

Echinoderm Larvz and their Bearing on 
Classification. 
‘THouGH loth to prolong this discussion, I wish, in 
fairness to Dr. Mortensen and myself, to say that 
I did not accuse Dr. Mortensen of regarding the 
echinoderm metamorphosis as a case of metagenesis, 
What I did write in Narure for December 8, 1921, 
— to ey. with Dr. Mortensen’s state- 
ent on March 10, 1923—a statement 
Prof. MacBride. oe pasha 
NO. 2786, VoL. 111] 
Against Dr. Mortensen’s view, that the sucking disc 
of Brachiolaria is a relatively recent acquisition, 
Prof. MacBride would cite me as in substantial 
agreement with himself (NATURE, January 13). That 
agreement extends to our common belief that all 
groups of echinoderms have passed through a fixed 
stage at some time in their ancestral history. On 
the precise relation of that fixed stage to the adult 
structure in the case of the starfish, we do not agree, 
Dr. Mortensen, it appears, is one of those who support 
my particular view. The sucking disc of the Brachio- 
laria has certainly been regarded by me, as by Prof. 
MacBride, as confirmatory evidence of the general 
theory. But if, as Dr. Mortensen now suggests, it 
be a secondary development, the theory does not 
necessarily fall, and Dr. Mortensen distinctly says 
that it does not. On the other hand, assuming Dr. 
Mortensen to be correct in his assertion that the 
forms with such a larva are only the more specialised, 
the sucker may none the less perpetuate an ancestral 
structure. 
Until the geological history of the starfishes has 
been more fully worked out along the lines followed 
by Dr. W. K. Spencer, it is safer to express no opinion 
on the classification of the forms now living. 
F. A. BATHER. 
March 11. 
Constitution of Black Maketu Sand. 
WE have made a careful chemical and X-ray 
analysis of the black sand from Maketu, N.Z., from 
which Dr. Alexander Scott believed he had isolated 
the oxide of a new element. We are able to confirm 
Prof. Bohr’s conclusion that no new element is present. 
Starting with 1000 grams of the sand we obtained 
I-7 grams of material free from silica, and insoluble 
in sulphuric acid. Fusion with sodium bisulphate 
did not bring this into solution, thus confirming Dr. 
Scott’s experience, but it is interesting to note that 
on fusion with potassium bisulphate the residue went 
into solution completely, and was found by both 
chemical and X-ray analysis to consist of about 
equal parts of iron and aluminium. Prof. Bohr 
found an appreciable quantity of titanium in the 
residue, while we found no more than a trace ; but as 
our residue was only o-2 per cent of the ore our 
extraction was probably more complete. 
C. J. SMITHELLs. 
F. S. GOUCHER. 
Research Laboratories, 
General Electric Co., Ltd., 
Wembley, March 8. 

Scientific Periodicals for Czech Students. 
I HAVE recently received a most earnest and pathetic 
request from a group of Czech students at the Uni- 
versity of Prague asking me whether this Society could 
send them an English scientific periodical. Unfortun- 
ately we have no funds for this, but it has struck me 
that it might be possible for some of your subscribers, 
who perhaps do not have their copies of NATURE 
bound, to let me have them to send to these students. 
It would be a really kind and charitable act, and 
would be helpful in promoting the good feeling between 
ourselves and the Czecho-Slovaks, which is so useful 
at the present time. 
If the papers were to be sent from London, I could 
arrange to call for them at stated times, so that no 
trouble of packing or postage would be involved. 
B. O. TUFNELL. 
The Czech Society of Great Britain, 
Kensington Palace Mansions, W.8, March 2. 
M2 
